So a friend of mine came up with an interesting question. Considering the fairly universal following facts about western-style fantasy dragons:

a) dragons can breath fire

b) dragons themselves are fireproof

c) dragons have large wings, allowing them to fly (though the actual science of this is well-known to be fishy, let's for now pretend a dragon such as Toothless or Smaug can actually fly. Super light bones or whatever.)

d) hot air rises and creates lift

If the dragon can produce a large quantity/sizable blast of extremely high heat, could it be useful to the dragon for it napalm/torch the ground beneath it as it was taking off, in order to create additional lift for itself? Or would the effect of doing this be so negligible that it wouldn't be worth it to bother?

Unlikely if not impossible. The lift created by heat (pressure differences) is different than the lift created by the wings (mechanical). The "help" given by one is unlikely to help the other - and the difference would likely be negligible.

Mechanical Lift

Lift as a mechanical force is created by motion. Here is a good explanation, and Wikipedia has a decent article on lift. You can read more about how birds create lift here.

Pressure Lift

Lift by pressure differences is how hot balloons work - but this is because of the density of the balloon (here, dragon) in relation to the surrounding air. Unless the dragon could contain the heat entirely beneath it, the heat would dissipate very rapidly - especially if it is significantly hotter than the air around it. This would make for a very bad way to create lift.

Cannons

I suppose, in theory, if a dragon was stuck upside-down inside a pipe, then a good heave might push it out. But this would be more like how cannons and firearms work than any concept of actual lift. In such a scenario, the dragon would be "pushed" out, and could then flap it's wings - assuming that it could create enough of an explosion (fireball) to force itself loose.

Thermal Soaring

I think its possible:

• Birds like raptors (eagles/hawks etc), vultures, and storks can gain altitude without flapping by hopping a ride on a rising column of warm air. This is called Thermal Soaring.


• We assume (according to your point c) that dragons can fly reasonably well, but can they soar? Soaring ability in dragons seams likely, as dragons are typically thought of as carnivores which means they have to fly around looking for prey to catch (like eagles/hawks) or fly around looking for dead prey (vultures/condors). All that flying around means you need to be energy efficient and be able to soar. If dragons are capable of soaring in general, then they should be capable of thermal soaring as well.


• According to my googling, wildfires can cause thermal columns.

Thus, the dragon starts a wildfire, takes off for flight (likely by jumping up like giant pterosaurs) and flaps a few times to get in the air over the wildfire, and then can thermal soar up high.